Mathematics, 30.01.2022 22:30 megamorph

The angle of elevation to a nearby tree from a point on the ground is measured to be 69^{\circ} ∘
. How tall is the tree if the point on the ground is 35 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.

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Answer from: vrentadrienneoqug1a

The tree is approximately 91.2 ft tall.

Step-by-step explanation:

Hi there!

We're told:

- angle of elevation = 69 degrees

- there is a point 35 feet from the tree

If we were to draw this out, it would appear to be a right angle triangle. See the picture below.

Now, to solve for the height of the tree, we can use the sine law:

$\frac{a}{ \sin(a) } = \frac{b}{ \sin(b) }$

where a and b are two sides of a right triangle and A and B are the respective opposite angles

Let the height of the tree = h.

Side h is opposite of the angle measuring 69 degrees:

$\frac{h}{ \sin {69}^{o} }$

Let the angle opposite of the side measuring 35 feet = A.

$\frac{35}{ \sin(a) }$

Because the sum of a triangle's interior angles is 180 degrees, we know that A=180-90-69=21 degrees.

$\frac{35}{ \sin {21}^{o} }$

Use the sine law:

$\frac{h}{ \sin {69}^{o} } = \frac{35}{ \sin {21}^{o} }$

$h = \frac{35}{ \sin {21}^{o} } \: \sin {69}^{o}$

h = 91.17812

Therefore, the tree is approximately 91.2 ft tall.

I hope this helps!

Answer from: Quest

answer: the answer is one of

$f=\dfrac{1}{2},~\dfrac{1}{4},~\dfrac{3}{4},~\dfrac{1}{6},~\dfrac{5}{6},~\dfrac{1}{8},~\dfrac{3}{8},~\dfrac{5}{8},~\dfrac{7}{8}.$

step-by-step explanation: we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

$f=\dfrac{1}{2},~\dfrac{1}{4},~\dfrac{3}{4},~\dfrac{1}{6},~\dfrac{5}{6},~\dfrac{1}{8},~\dfrac{3}{8},~\dfrac{5}{8},~\dfrac{7}{8}.$

Answer from: Quest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

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